Fluid Stimulation of Long Well Intervals

ABSTRACT

Systems and methods for accessing and/or harvesting hydrocarbons from a wellbore. A method may include modeling a well to determine a length of a stimulation zone in the production interval, wherein the model is based, at least in part, on a reaction time for a stimulation process. Packers are placed in the well to fluidically isolate the stimulation zone from other zones in the well. The targeted zone is stimulated, such as by acid treatment. Hydrocarbons may be recovered from the stimulation zone.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional No. 61/569,557, filed Dec. 12, 2011.

FIELD

The present techniques relate to completions of horizontal wells. Specifically, techniques are disclosed for fluid stimulation in long horizontal wells.

BACKGROUND

This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present techniques. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present techniques. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.

Modern society is greatly dependent on the use of hydrocarbons for fuels and chemical feedstocks. Hydrocarbons are generally found in subsurface rock formations that can be termed “reservoirs.” Removing hydrocarbons from the reservoirs depends on numerous physical properties of the rock formations, such as the permeability of the rock containing the hydrocarbons, the ability of the hydrocarbons to flow through the rock formations, and the proportion of hydrocarbons present, among others.

As many newer reservoirs are located in challenging environments, such as in very deep oceanic environments, production methods increasingly rely on long (˜1,000′) and ultra long (˜10,000′) open hole, horizontal well (OHHW) completions. These horizontal completions can be drilled from a single platform or rig to reach numerous locations in a reservoir. After drilling, the production rates of the completions can be further improved by stimulation. Stimulation is a process by which the flow of hydrocarbons between a formation and a well is enabled and/or improved. This can be performed by any number of techniques, such as fracturing a rock within the well with a high pressure fluid, injecting a surfactant into a well, or injecting steam to lower the viscosity of the hydrocarbons. One technique uses an acid injection into the well, which can increase flow from the formation into the well. Such improvement can happen because of wormholes connecting the well to a larger extent of the formation. Wormholes are small holes or cracks formed by acid attack on certain types of rock.

Nearly half of the world reserves are contained in carbonate formations, which can be effectively stimulated by acid injection. Acid placement is important for a successful acid treatment of a matrix. However, acid will generally flow into areas of least resistance, e.g., into areas of high permeability. This is opposed to the main objective of the matrix treatment, which is to increase the productivity of low permeability zones. Numerous mechanical and chemical diversion methods have been developed to place acid in the desired areas of the formation around the well. Mechanical methods make use of various bridge plugs, packers, ball sealers and their combination. Chemical diversion utilizes various chemical systems designed to make acid interact with the formation in the area of interest. Chemical systems used for diversion can include salt granules, waxes, foam, viscous pills, and the like.

U.S. Patent Application Publication No. 2009/0114385, by Lumbye, discloses a method of stimulating a well. In the method, a tubular is introduced into a wellbore and cemented into place. The tubular is then perforated at pre-selected locations. The locations of the perforations are selected by modeling inflow performance of a stimulation fluid within the formation. The inflow performance parameters can include reservoir porosity, permeability, pressure, damage skin and intrusion depth, perforation diameter and penetration depth, or perforation crushed zone damage and intrusion depth.

U.S. Pat. No. 7,748,460, to Themig, discloses a method and apparatus for wellbore fluid treatment. An apparatus includes a tubing string assembly for fluid treatment of a wellbore. The tubing string assembly includes pressure holding closures spaced along the tubing string. Each closure can close at least one port through the tubing string wall. The closures are openable by a sleeve drivable through the tubing string inner bore.

The disclosures described above can target locations in a well for contact with a stimulation fluid. However, neither describes modeling relations between the length of production intervals and the inflow of stimulation fluids in a wellbore to improve the effectiveness of stimulation.

SUMMARY

An embodiment described herein provides a method for fluid stimulation of long well intervals. The method includes drilling a well to reach an interval within a reservoir. Locations for packers are selected to fluidically isolate zones in the interval, wherein the selection is based, at least in part, on a model of the response of a rock to a stimulation fluid over a period of time. The packers are positioned at the selected locations and stimulating the reservoir within selected zones using an acid solution. The methods include processes for actually performing the operation, as well as processes for modeling or planning such operations in conjunction with preparing a well completion or well construction plan.

Another embodiment provides a system for fluid stimulation in wells. The system includes a well drilled through an interval in a reservoir and a plurality of packers placed in the well. A zone is defined by the location of two sequential packers in the well, and the location of each of the plurality of packers is selected from a model of wormhole growth dynamics and flow of stimulation fluid in the well over time during an acid stimulation procedure. A well string is configured to convey acid to a zone in the production interval.

Another embodiment provides a method for harvesting hydrocarbons from a production interval. The method includes modeling a well to determine a length of a stimulation zone in the production interval, wherein the model is based, at least in part, on a reaction time for a stimulation process. Packers are placed in the well to fluidically isolate the stimulation zone from other zones in the well. The zones are stimulated by acid treatment and hydrocarbon is recovered from the stimulation zone.

DESCRIPTION OF THE DRAWINGS

The advantages of the present techniques are better understood by referring to the following detailed description and the attached drawings, in which:

FIG. 1 is a drawing of a well drilled to reservoir, wherein the well has a significant horizontal section that extends through multiple rock types in the formation;

FIG. 2 is a drawing of a zone of a wellbore showing the uneven growth of wormholes due to restimulation effects;

FIG. 3 is a drawing of an interval of a wellbore showing the installation of packers to isolate zones from each other;

FIG. 4 is a drawing of an interval showing a more even growth of wormholes in a zone that is isolated by packers;

FIG. 5 is a drawing of a well through an interval that has multiple rock types;

FIG. 6 is a process flow diagram of a method for stimulating a well by modeling the stimulation dynamics to determine appropriate lengths for stimulation zones;

FIG. 7 is a block diagram of an exemplary cluster computing system that may be used to implement models for the present techniques;

FIG. 8 is a schematic showing the growth of a wormhole into volume regions, or computational cells, adjacent to a well;

FIGS. 9(A) and (B) are plots illustrating the calculation of an efficiency curve for the stimulation;

FIG. 10 is a schematic illustrating an apparatus for calibrating a model of wormhole growth, such as that described above; and

FIG. 11 is a plot showing a comparison of the results obtained from the model versus experimental results at two different flow rates.

DETAILED DESCRIPTION

In the following detailed description section, specific embodiments of the present techniques are described. However, to the extent that the following description is specific to a particular embodiment or a particular use of the present techniques, this is intended to be for exemplary purposes only and simply provides a description of the exemplary embodiments. Accordingly, the techniques are not limited to the specific embodiments described below, but rather, include all alternatives, modifications, and equivalents falling within the true spirit and scope of the appended claims.

At the outset, for ease of reference, certain terms used in this application and their meanings as used in this context are set forth. To the extent a term used herein is not defined below, it should be given the broadest definition persons in the pertinent art have given that term as reflected in at least one printed publication or issued patent. Further, the present techniques are not limited by the usage of the terms shown below, as all equivalents, synonyms, new developments, and terms or techniques that serve the same or a similar purpose are considered to be within the scope of the present claims.

“Facility” as used in this description is a tangible piece of physical equipment through which hydrocarbon fluids are either produced from a reservoir or injected into a reservoir, or equipment which can be used to control production or completion operations. In its broadest sense, the term facility is applied to any equipment that may be present along the flow path between a reservoir and its delivery outlets. Facilities may comprise production wells, injection wells, well tubulars, wellhead equipment, gathering lines, manifolds, pumps, compressors, separators, surface flow lines, steam generation plants, processing plants, and delivery outlets. In some instances, the term “surface facility” is used to distinguish those facilities other than wells.

As used herein, two locations in a reservoir are in “fluid communication” when a path for fluid flow exists between the locations. For example, the drilling of a wellbore through a formation will place different formation locations along the wellbore in fluid communication with each other. As used herein, a fluid includes a gas or a liquid and may include, for example, a produced hydrocarbon or an injected stimulation fluid, among other materials. Similarly, two locations can be “fluidically isolated” from each other to create zones along the wellbore by any number of techniques, including the placement of packers in an annulus between a production liner and a wellbore, the collapse of the formation around the wellbore, and other techniques.

The term “formation” refers to a body of rock or other subsurface solids that is sufficiently distinctive and continuous that it can be mapped. A formation can be a body of rock of predominantly one type or a combination of types. A formation can contain one or more hydrocarbon-bearing zones. Note that the terms “formation,” “reservoir,” and “interval” may be used interchangeably, but will generally be used to denote progressively smaller subsurface regions, volumes, or zones. More specifically, a “formation” will generally be the largest subsurface region, a “reservoir” will generally be a region within the “formation” and will generally be a hydrocarbon-bearing zone (a formation, reservoir, or interval having oil, gas, heavy oil, and any combination thereof), and an “interval” will generally refer to a sub-region or portion of a “reservoir.” An interval, as used is herein, is a specific portion of a reservoir that is accessed by a well, such as an open hole horizontal well (OHHW). Further, a “zone” is used herein to refer to a portion of an interval along a wellbore that is fluidically isolated from other portions, such as by a packer. As used herein, fluidically isolated merely refers to flow through the well or through an annulus along the well. It does not indicate that fluid flow through the rock of the interval itself is blocked.

A “hydrocarbon” is an organic compound that primarily includes the elements hydrogen and carbon, although nitrogen, sulfur, oxygen, metals, or any number of other elements may be present in small amounts. As used herein, hydrocarbons generally refer to components found in heavy oil, or other oil sands.

As used herein, a “model” is a computer-based representation of one or more physical properties throughout a subsurface earth volume, such as a depositional basin, a reservoir, an interval, or along a well. Geologic models may take on many different forms. Depending on the context, descriptive or static geologic models built for petroleum applications can be represented in 1-D, 1.5-D, 2-D, 2.5D, 3D and the like. Some examples of earth material properties include conductivity, resistivity, or, in the case of an anisotropic earth, horizontal conductivity and vertical conductivity. Further, the model can include porosity, permeability, flow data, and combinations thereof. The model can be used to perform numerous functions for developing hydrocarbon resources, such as locating a well in an interval within a reservoir, for example, with respect to other wells drilled to the reservoir. In embodiments described herein, the model can be used to determine the placement of packers along a well to select the length of zones for stimulation and to isolate zones in rock that may use different stimulation parameters.

As used herein, “packers” are a type of sealing mechanism used to block the flow of fluids through a well or an annulus within a well. Packers can include open hole packers, such as swelling elastomers, mechanical packers, or external casing packers, which can provide zonal segregation and isolation. Multiple sliding sleeves can also be used in conjunction with open hole packers to provide considerable flexibility in zonal flow control for the life of the wellbore. As used herein, the term “packers” also includes any other sealing mechanisms that can be used for zonal isolation and segregation, such as plugs, sliding plugs, ball sealing mechanisms, and any other sealing mechanism that can be used to isolate zones, such as a cement plug in an annulus.

“Permeability” is the capacity of a rock to transmit fluids through the interconnected pore spaces of the rock. Permeability may be measured using Darcy's Law: Q=(k ΔP A)/(μL), wherein Q=flow rate (cm³/s), ΔP=pressure drop (atm) across a cylinder having a length L (cm) and a cross-sectional area A (cm²), μ=fluid viscosity (cp), and k=permeability (Darcy). The customary unit of measurement for permeability is the millidarcy. The term “relatively permeable” is defined, with respect to formations or portions thereof, as an average permeability of 10 millidarcy or more (for example, 10 or 100 millidarcy).

“Porosity” is defined as the ratio of the volume of pore space to the total bulk volume of the material expressed in percent. Porosity is a measure of the reservoir rock's storage capacity for fluids. Porosity is preferably determined from cores, sonic logs, density logs, neutron logs or resistivity logs. Total or absolute porosity includes all the pore spaces, whereas effective porosity includes only the interconnected pores and corresponds to the pore volume available for depletion.

“Substantial” when used in reference to a quantity or amount of a material, or a specific characteristic thereof, refers to an amount that is sufficient to provide an effect that the material or characteristic was intended to provide. The exact degree of deviation allowable may depend on the specific context.

A “wellbore” or “well” is a hole in the subsurface made by drilling or inserting a conduit into the subsurface. A wellbore may have a substantially circular cross section or any other cross-sectional shape, such as an oval, a square, a rectangle, a triangle, or other regular or irregular shapes. As used herein, the term “wellbore”, may refer to the entire hole from the surface to the toe or end in the formation, or may refer to a subsection, such as a substantially horizontal section located in an interval within a reservoir. Further, the term “wellbore” may refer to a tubular construct configured to convey fluids to and from a subsurface formation. Further, the term wellbore may be used as a general term to describe any portion of the construction, from the surface to a horizontal production interval. The “wellbore” often ends in a “production liner” which is a tubular that is configured to convey fluids to and from the adjacent portion of the wellbore. These terms are used for simplicity of explanation. It will be clear to those of ordinary skill in the art that the techniques described herein may be used in any number of other completion configurations.

As used herein, a “wormhole” is a high permeability channel that starts from a wellbore and propagating into an interval in a reservoir. In addition to forming naturally in some types of formation, wormholes can be generated during well stimulation processes by any number of techniques. For example, a reactive fluid such as an acid may be used to generate wormholes in a carbonate formation. The development of wormholes may substantially enhance production in intervals within reservoirs.

Overview

Ultra long (1,000-10,000′), open hole, horizontal wells (OHHW) have become increasingly common as they allow a larger contact zone with a reservoir combined with a favorable production index. Production index is a ratio of well production rate to a drawdown, which is the difference between pressure in the reservoir and at the bottom of the well. Higher production index is more favorable, indicating a lower resistance to the flow from the reservoir to the well. Acid stimulation of such wells can greatly enhance their productivity and may remedy many flow impairment mechanisms later in the well's life, such as scale, fines, condensate formation, non-Darcy effects, and the like. A non-Darcy effect is an additional resistance to flow in the formation due to an inertial effect and may often be found in high production gas wells. The acid can be delivered to a production interval using any number of tubulars, such as production tubing, drill pipe or coiled tubing.

However, production intervals of such long lengths offer a unique challenge for acid placement. In particular, the time it takes to fill the wellbore with the acid at currently available flow rates is comparable to the stimulation time required to place determined amount of acid per unit of formation length. Hence, acid injected at the later stages of stimulation tends to flow into the wormholes already created at the previous stages. This effect, termed “restimulation,” leads to uneven growth of the wormholes in the formation.

In many cases, coiled tubing (CT) assisted acid placement may provide more versatility in selecting the zone treatment than other techniques. For this reason, CT acid placement has often been selected for stimulating long OHHWs, because it creates a relatively low local moving source of radial velocity. Such an injection can provide a better exposure of the formation face to the normal acid flow and, thus, to a better acid utilization.

However, the use of CT may be problematic at longer production intervals. Due to CT pump rate limitations and a large formation area to be stimulated, the CT stimulation time can exceed twenty hours. Acid corrosion protection of the equipment can be challenging at these long contact times. Furthermore, corrosion of the CT string may lead to problematic consequences such as equipment lost in the well and acid leaks downhole or at the surface. In addition to these problems, acid stimulation over such a long time-frame can lead to significant restimulation, leading to uneven growth of wormholes into the formation. Moreover, completion operations are taking place in increasingly remote areas, which may lead to a situation where getting long enough CT is not practical due to logistics, such as cost, weight, size, and the like.

Delivering the acid through the drill pipe (DP) or production tubing provides a high acid flow rate, for example, up to about 20 bpm, as well as the ability to transport solids and a higher resistance to corrosion. Drill pipe will also be available even in remote areas. However, injecting acid though a DP can also lead to a restimulation effect. Such an effect is unique to long OH wells when the time of acid spread in an axial direction is similar to the formation time for wormholes. In this case, the acid will preferentially flow into wormholes created earlier, leading to a non-uniform stimulation which is detrimental to the performance of the well. Therefore, acid placement through DP that takes advantage of high acid flow rates while avoiding the restimulation effect would be useful.

Accordingly, embodiments described herein provide a method for improving recovery from a subsurface hydrocarbon reservoir. More specifically, embodiments provide a method of high rate, efficient acid stimulation of ultra long horizontal open hole wells, for example, for stimulating intervals ranging in length up to several thousands of feet. A model is used to determine the locations for packers to isolate zones in the well that are upstream and downstream of the stimulation zone. After the well is drilled, the packers are placed to isolate the zones so that zones that are first stimulated are protected during the stimulation of later zones. The targeted zone is stimulated using a high rate of acid flow.

FIG. 1 is a drawing 100 of a well 102 drilled to reservoir 104, wherein the well 102 has a significant horizontal section 106 that extends through multiple rock types 108 in the formation. A well head 110 couples the well 102 to other apparatus that can be used for the stimulation, such as a pump 112 and an acid reservoir 114. The multiple rock types 108 may include a number of different types formed by changes in the deposition environment. For example, a reservoir 104 may have mostly carbonate rock layers 116, 118, and 120, but may also have one or more cemented sand layers 122. As noted, the length of the horizontal section 106 of the well 102 may be long enough that significant restimulation occurs, leading to uneven growth of wormholes along the well. Thus the horizontal section 106 may be divided into multiple zones that are individually stimulated, based on a model of the rock response and stimulant flow rates.

In addition, different layers of rock may respond differently to the stimulation. For example, the carbonate rock layers 116-120 may respond differently to acid stimulation than the cemented sand layer 122. Further, even the different carbonate rock layers 116-120 may have different responses to the acid stimulation, indicating that different stimulation times and parameters may be effective. In some cases, higher permeability rock layers may not need stimulation.

Although acid is described as the stimulation fluid herein, other stimulation fluids may be used in embodiments, depending on rock solubility. For example, in some embodiments, water or a weak acid solution may be sufficient.

FIG. 2 is a drawing of a zone 200 of a wellbore 202 showing the uneven growth of wormholes 204 due to restimulation effects. Modeling has revealed that the large volume of ultra long OHHWs and the limited acid injection rate, of about 20 bpm, through drill pipe 206 inserted in a predrilled liner 208 can lead to problems with restimulation. More specifically, in an ultra long well the time scale of the axial acid propagation 210 along the wellbore 202 is similar to time of growth for wormholes 204. This means that acid injected at the later stages of stimulation will be diverted into zones 212 already stimulated, causing restimulation instead of stimulating new zones.

The result is highly uneven stimulation of the production zone that may leave a significant part of the open hole unstimulated. Modeling has indicated that restimulation is the single most important effect, while the permeability contrast of the original formation is not as important. Injection of acid through an open-end drill pipe 206 or through a drill pipe 206 into a liner 208 with predrilled side holes 214 may not show significant difference, restimulation can still dominate the acid placement.

As an example, the wellbore 202 may be a 10,000′ OHHW, which is to be stimulated by acid flow through a drill pipe 206 into a predrilled liner 208 to facilitate radial flow. The acid placement flows from the toe 216 of the well 202 to the heel 218 of the well 202. The acid placement can be separated into 20 stages. At each stage, 15% concentration HCl acid can be pumped into the wellbore 202 at 20 bpm for six minutes, placing 120 bbl. of acid per stage. After each stage the drill pipe can be moved 500 ft. towards the heel and another stage of the injection can be performed. Such treatment provides for 10 gal of acid per foot of the formation.

However, the flow lines 210 show that, without packers or other techniques to isolate intervals, the acid flows mainly into already stimulated zones 212 of the formation and leaves large areas 220 of the formation having minimal or no stimulation. Even at the later stages of the stimulation the acid will still flow to the toe due to low resistance of already stimulated areas.

FIG. 3 is a drawing of an interval 300 of a wellbore 302 showing the installation of packers to isolate zones from each other. The packers can include preinstalled packers 304 placed in the annulus 306 between a liner 308 and the wellbore 302. Further, retractable packers 310 may be used in the annulus 312 between the liner 308 and a drill pipe 314. Holes 316 can be predrilled in the liner 308 to allow fluids to flow between the wellbore 302 and the tubulars, such as the liner 308 and drill pipe 314. In an embodiment, the preinstalled packers may be, for example, about 10′ in length 318, to isolate the zones 320 and improve acid placement within OHHWs. The long packers 304 may assist in decreasing the amount of stimulation fluid that passes between zones 320 via the rock to the wellbore 302.

Any number of other techniques may be used to isolate the zones 320 in embodiments. In some embodiments, soluble plugs may be used to temporarily block portions of the liner, so that zones may be stimulated. The plugs may be acid soluble, for example, made from salts that dissolve at known rates or polymers that degrade at known rates. In some embodiments, removable plugs may be used to isolate portions of the liner from other portions of the liner to create the zones for stimulation. Ball-and-seat plugs may also be used to isolate portions in some embodiments.

FIG. 4 is a drawing of an interval 400 showing a more even growth of wormholes 402 in a zone 404 that is isolated by packers 304 and 310. In FIG. 4, like numbers are as discussed with respect to FIG. 3. A model is used to select the distance between the packers 304 and 310 to effectively reduce the length of stimulated zone 404, significantly reducing the restimulation effect. Other parameters may also be selected using the model, such as the number and spacing of holes 316 in the liner 308.

The use of the packers 304 and 310 essentially decreases the volume of the wellbore 302 for the stimulation procedure. As an illustration, in the example discussed with respect to FIG. 2, packers 304 and 310 can be placed at about 165 m (about 500′) apart and the stimulation area is essentially the same as a short well of about the same length. A high acid flow rate through the drill pipe within about 165 m (about 500′) stimulated interval results in a substantially uniform stimulation. The modeling indicates that packers 304 should be of sufficient length, for example, about 3 m to 6.5 m (about 10 to 20 feet) in length, so the acid will not bypass them through the formation.

FIG. 5 is a drawing 500 of a well 502 through an interval 504 that has multiple rock types. In the drawing 500, packers 506 have been placed to isolate zones, such as zones 508, for stimulation. Although differing rock types may have differing permeabilities and porosities, as noted, the most important effect is restimulation.

Thus, the length of the zones 508 in stimulation intervals 510 can be more important than isolating rocks of different types. For this reason, different rock types may be included in a single zone 508. However, if a rock type 512 is sufficiently different in response to the acid stimulation from other rock types 514, the model results may indicate the value of using a packer 516 to isolate this rock type 512 into isolated stimulation zones 518 that are acid stimulated using a different set of parameters.

Some rock types 520 may be sufficiently permeable or naturally fractured that no stimulation is needed to increase the flow. These rock types may be isolated by packers 522 and used for production without further stimulation. The packers 522 used to isolate the permeable zones 524 may be longer to lower the amount of the stimulation fluid that flows around the packers 522 into the permeable zones 524 from adjacent zones, such as zones 508, that are being stimulated.

Stimulation Method

FIG. 6 is a process flow diagram of a method 600 for stimulating a well by modeling the stimulation dynamics to determine appropriate lengths for stimulation zones. The method 600 begins at block 602 with the collection of data needed to model the reservoir. Such data may include geophysical data collected by seismic measurements and seismic inversions, well log data, electromagnetic data, gravimetric data, and the like. At block 604, the model can be used to map the locations of the reservoir and the production intervals. At block 606, the model can be used to locate a well within an interval, for example, to maximize the potential for hydrocarbon production. The well can include an OHHW section that passes through the production interval. Once located in the production interval, at block 608, the well is drilled in the production intervals. During drilling, core samples can be taken along the well, which are used at block 610 to determine the porosity, permeability, and chemistry of the rock.

At block 612, the information collected from the well can be used to determine lengths for stimulation zones along the well, in addition to rock types that may need no stimulation or different stimulation parameters. The lengths of the stimulation zones and the rock type determinations can be used to locate packers, or other isolation devices, along the well to fluidically isolate each of the zones from adjacent zones. As noted herein, the fluidic isolation is determined with respect to the wellbore, but some amount of stimulation fluid may flow around the isolation devices through the rock of the interval. To decrease the amount of stimulation fluid that bypasses the packers, longer packers may be used, as described herein. In one embodiment, a OHHW, for example of about 3300 m (about 10,000 ft.) can be drilled through an interval that includes similar rock types. As the most important effect in stimulation is the possibility of restimulation, the lengths of the zones may be more important than the variations in rock type. If a total of seven packers were able to be located in the well, each zone would be about 460 m (about 1,400 ft.) in length.

At block 614, the stimulation times for each zone are determined. The times may be different for different rock types and different zone lengths. In some embodiments, the stimulation times are determined by the relationship between the flow rates into the well and the reaction rates for the formation of wormholes. This dynamic relationship can be used to determine both zone lengths and stimulation times to obtain an even stimulation across the well.

At block 616, packers are placed in the well at the points determined by the model. This can be performed in conjunction with the placement of a liner, such as a predrilled pipe, in the well. At block 618, each zone is stimulated for the amount of time determined from the model. The stimulation can be performed using a drilling pipe inserted down the liner into each zone, which can be isolated from other zones by an expandable liner placed in the annulus between the drilling pipe and the liner. Other packers, temporary plugs, and the like, may be used to isolate zones in addition to the packers described. Once the stimulation is completed, the stimulation fluids may be cleared from the well. At block 620, hydrocarbons are produced from the well.

FIG. 7 is a block diagram of an exemplary cluster computing system 700 that may be used to implement models for the present techniques. The cluster computing system 700 illustrated has four computing units 702, each of which may perform calculations for part of the geologic and flow models. However, one of ordinary skill in the art will recognize that the present techniques are not limited to this configuration, as any number of computing configurations may be selected. For example, a smaller model may be run on a single computing unit 702, such as a workstation, while a large model may be run on a cluster computing system 700 having 10, 100, 1000, or even more computing units 702.

The cluster computing system 700 may be accessed from one or more client systems 704 over a network 706, for example, through a high speed network interface 708. The network 706 may include a local area network (LAN), a wide area network (WAN), the Internet, or any combinations thereof. Each of the client systems 704 may have non-transitory, computer readable memory 710 for the storage of operating code and programs, including random access memory (RAM) and read only memory (ROM). The operating code and programs may include the code used to implement all or any portions of the methods discussed herein, for example, as discussed with respect to FIGS. 6 and 8-11. Further, the non-transitory computer readable media may hold full state checkpoints, correlation checkpoints, and simulation results, such as a data representation of a subsurface space. The client systems 704 can also have other non-transitory, computer readable media, such as storage systems 712. The storage systems 712 may include one or more hard drives, one or more optical drives, one or more flash drives, any combinations of these units, or any other suitable storage device. The storage systems 712 may be used for the storage of checkpoints, code, models, data, and other information used for implementing the methods described herein. For example, the data storage system may hold checkpoints for the model.

The high-speed network interface 708 may be coupled to one or more communications busses in the cluster computing system 700, such as a communications bus 714. The communication bus 714 may be used to communicate instructions and data from the high-speed network interface 708 to a cluster storage system 716 and to each of the computing units 702 in the cluster computing system 700. The communications bus 714 may also be used for communications among computing units 702 and the storage array 716. In addition to the communications bus 714 a high-speed bus 718 can be present to increase the communications rate between the computing units 702 and/or the cluster storage system 716.

The cluster storage system 716 can have one or more non-transitory, computer readable media devices, such as storage arrays 720 for the storage of checkpoints, data, visual representations, results, code, or other information, for example, concerning the implementation of and results from the methods of FIGS. 6 and 8-11. The storage arrays 720 may include any combinations of hard drives, optical drives, flash drives, holographic storage arrays, or any other suitable devices.

Each of the computing units 702 can have a processor 722 and an associated local tangible, computer readable media, such as memory 724 and storage 726. Each of the processors 722 may be a multiple core unit, such as a multiple core CPU or a GPU. The memory 724 may include ROM and/or RAM used to store code, for example, used to direct the processor 722 to implement the methods discussed with respect to FIGS. 6 and 8-11. The storage 726 may include one or more hard drives, one or more optical drives, one or more flash drives, or any combinations thereof. The storage 726 may be used to provide storage for checkpoints, intermediate results, data, images, or code associated with operations, including code used to implement the method of FIGS. 6 and 8-11.

The present techniques are not limited to the architecture or unit configuration illustrated in FIG. 7. For example, any suitable processor-based device may be utilized for implementing all or a portion of embodiments of the present techniques, including without limitation personal computers, networks personal computers, laptop computers, computer workstations, GPUs, mobile devices, and multi-processor servers or workstations with (or without) shared memory. Moreover, embodiments may be implemented on application specific integrated circuits (ASICs) or very large scale integrated (VLSI) circuits. In fact, persons of ordinary skill in the art may utilize any number of suitable structures capable of executing logical operations according to the embodiments.

Modeling of Wormhole Growth Dynamics

FIG. 8 is a schematic 800 showing the growth of a wormhole 802 into volume regions, or computational cells 804 and 806, adjacent to a well 808. The partitioning of a well and a surrounding formation region into discrete volumes or computational cells is a widely used numerical method in Computational Fluid Dynamics (CFD).

For purposes of the model, each cell 804 and 806 is assumed to have a certain length, L 810. The wormhole 802 grows through the rock of the cells 804 and 806, with a pressure gradient 812 represented by Eqn. 1 also known as Darcy's law.

$\begin{matrix} {{\Delta \; p} = \frac{\mu_{f}{\overset{\rightarrow}{U}}_{f}}{k({wormhole})}} & {{Eqn}.\mspace{14mu} 1} \end{matrix}$

In Eqn. 1, ∇p represents the pressure gradient through the wormhole 802, μ_(f) represents the viscosity of the treatment solution, {right arrow over (U)}_(f) represents the superficial flow velocity vector, i.e., the magnitude and the direction of the fluid flow rate in rock pores per unit of the total formation area. Effective permeability k(wormhole)=k_(eff) is determined by any number of factors. However, in the present example, the most important factors are location, extent, and growth dynamics of the wormholes. Such dependency of the permeability on wormhole dynamics may be determined by experimental measurements on samples of the rock obtained from cores from the well.

The rate of mass accumulation of the acid in the wormhole 802 can be represented by Eqn. 2.

$\begin{matrix} {\frac{D\left( {\rho_{j}Y_{HCL}} \right)}{Dt} = {{{- \nabla} \cdot \left( {{\nabla D_{HCL}}Y_{HCL}} \right)} - {{h_{m}\left( {Y_{HCL} - Y_{{HCL},{face}}} \right)}\frac{{Wormhole}\mspace{14mu} {area}}{{Volume}\mspace{14mu} {unit}}}}} & {{Eqn}.\mspace{14mu} 2} \end{matrix}$

In Eqn. 2, ρ_(f) represents the density of the stimulation fluid and Y_(HCl) represents the mass fraction of an HCl solution in stimulation fluid. On the opposite side of the equation, −∇·(∇D_(HCL)Y_(HCL)) represents the diffusion rate of HCl in water. The second term in the equation,

${{- {h_{m}\left( {Y_{HCl} - Y_{{HCl},{face}}} \right)}}\frac{{Wormhole}\mspace{14mu} {area}}{{Volume}\mspace{14mu} {unit}}},$

represents the consumption of HCl by rock dissolution, and is assumed to be negligible for purposes of the model.

The volume fraction of the wormhole 802, ε_(w), assuming all acid in the wormhole 802 is at the same concentration as the inlet, is shown in Eqn. 3.

$\begin{matrix} {ɛ_{w} = \frac{Y_{HCl}}{Y_{HCl}^{in}}} & {{Eqn}.\mspace{14mu} 3} \end{matrix}$

This can be used to determine the cell share occupied by wormhole 802, i.e., the volume fraction, where the function f is determined by experiments.

$\begin{matrix} {\frac{x}{L} = {f\left( ɛ_{w} \right)}} & {{Eqn}.\mspace{14mu} 4} \end{matrix}$

In Eqn. 3, x 814 is the length of penetration of a wormhole into a cell 806 and L 810 is the length of the cell 806, as noted previously. For example, the function may relate the length 814 of the wormhole in a cell 806 to the volume fraction of the wormhole 802 in the cell 806, as shown in Eqn. 5

$\begin{matrix} {\frac{x}{L} = {ɛ_{wh}^{p} = \left( \frac{Y_{HCl}}{Y_{HCl}^{in}} \right)^{p}}} & {{Eqn}.\mspace{14mu} 5} \end{matrix}$

Further, the effective permeability due to the wormhole 802 can be represented by Eqn. 6.

$\begin{matrix} {k_{eff} = \left( {\frac{\left( {Y_{HCl}/Y_{HCl}^{in}} \right)^{p}}{k_{w}} + \frac{\left( {1 - \left( {Y_{HCl}/Y_{HCl}^{in}} \right)} \right)^{p}}{k_{r}}} \right)^{- 1}} & {{Eqn}.\mspace{14mu} 6} \end{matrix}$

In Eqn. 6, the first term,

$\frac{\left( {Y_{HCl}/Y_{HCl}^{in}} \right)^{p}}{k_{w}},$

represents the contribution to effective permeability from the wormhole 802, while the second term,

$\frac{\left( {1 - \left( {Y_{HCl}/Y_{HCl}^{in}} \right)} \right)^{p}}{k_{r}},$

represents the contribution of the native rock. The power, p, is an implicit expression of the growth time scale for the wormhole 802. Thus, it is assumed to be a function of local velocity and known optimal velocity. The closer a local velocity is to an optimal value, the larger the value of p, and the faster the wormhole 802 grows.

Since power p in Eqn. 6 reflects wormhole growth time scale, it is related to the efficiency curve illustrated in FIG. 9(A), where the y-axis 902 is an acid volume needed to achieve a fixed wormhole length, as manifested by wormhole breakthrough. The acid volume is expressed in number of the rock pore volumes. The x-axis 904 of FIG. 9(A) is a stimulation fluid flow rate divided by a flowing surface area, i.e., superficial velocity U normalized by critical velocity defined below.

The efficiency curve in FIG. 9(A) can be represented by Eqn. 7.

eff=aU ⁻² +bU ^(1/3)  Eqn. 7

A term U_(crit) can represent the optimal (critical) superficial velocity leading to a most efficient wormhole growth. U_(crit) can be determined from Eqn. 8 as velocity at which the efficiency curve in FIG. 9(A) has a minimum.

U _(crit)=(6a/b)^(3/7)  Eqn. 8

In Eqn. 8, a and b represent coefficients that may be determined from experimental measurements on the type of rock. These coefficients depend on rock, temperature and acid type and concentration. The power term, p, can then be calculated using Eqns. 9 and 10.

p=5+35(U/U _(crit))² ,U/U _(crit)<1  Eqn. 9

p=5+35(U/U _(crit))^(−1/3) ,U/U _(crit)>1  Eqn. 10

In Eqns. 9 and 10, the flow velocity is parameterized as a unitless ratio, U/U_(crit), between the flow velocity and the optimal flow velocity.

The equations above may be used to develop a corresponding graph of power, p, as shown in FIG. 9(B). At U=U_(crit), the power, p, has a highest value of 40 corresponding to optimal acidization condition for the present conditions (acid type, rock, temperature etc.). As value of U gets further away from U_(crit), wormhole growth slows down which is reflected in lower value of power p as illustrated on FIG. 9(B). Such computations are performed at every computational cell representing the formation and characterized by local superficial velocity. Hence a local growth rate of a wormhole is implicitly computed by a computation of the value of the power p that is unique for each cell. Thus, the wormhole growth rate will be determined by a local velocity field at every location within the formation rock.

FIG. 10 is a schematic illustrating an apparatus 1002 for calibrating a model of wormhole growth, such as that described above. The apparatus 1002 has a rock sample 1004 that is selected to match a rock type in a formation. In this example, a hole 1006 is drilled through the center of the rock sample 1004 ending in an impenetrable plug 1008. The hole 1006 may be substantially smaller in diameter 1010 than the outer diameter 1012 of the rock sample 1004. The apparatus 1002 may be configured to pump an acid solution 1014, such as a solution of 15% HCl in water, into the hole 1006. Acid solution flows first axially in hole 1006 and then radially into the rock sample 1004 as illustrated by flow lines 1016 leading to a growth of wormholes 1018.

A pressure differential 1020 is measured between the outer surface of the rock sample 1006 and the hole 1008. As the wormholes 1018 grow through the rock sample 1004, the differential pressure 1020 decreases until a first wormhole reaches the outer boundary of sample 1004 (i.e., achieves breakthrough) at which point the pressure differential 1014 drops to zero. The measured volume of acid injected until breakthrough was achieved is used to construct the y-axis 902 of FIGS. 9(A) and (B) while the acid flow rate divided by surface of the hole 1008 (i.e., the superficial velocity) is used to construct the x-axis 904 of FIGS. 9(A) and (B). A number of experiments are conducted by flowing acid at different flow rates in each experiment to build an efficiency curve, such as shown in FIG. 9(A).

From a measured curve such as FIG. 9(A) the coefficients a and b and critical velocity U_(crit) can be determined for a given type of rock, type of acid, concentration of acid, and temperature of reaction.

FIG. 11 is a plot 1100 showing a comparison of the results obtained from the model versus experimental results at two different flow rates. The x-axis 1102 is the test time in minutes, while the y-axis 1104 is the pressure differential on a logarithmic scale. At a flow rate of 300 mL/min which was found to be close to U_(crit), the model results 1106 were in close agreement with the experimental measured points 1108 for the first minute, although the experimentally measured pressure differential fell faster after that time. At a flow rate of 800 mL/min, i.e., higher flow rate than U_(crit), the model results 1110 were is close agreement with the experimental measured points 1112 for the first three minutes, although the experimentally measured pressure differential fell faster after that time. Importantly, model was able to capture a faster pressure decline rate for optimal 300 mL/min injection rate. Thus, the model is able to predict observed dependence of wormhole growth rate on local acid velocity in formation.

Embodiments of the claimed subject matter may include the methods and systems disclosed in the following lettered paragraphs:

A. A method for fluid stimulation of long well intervals, including:

-   -   drilling a well to reach an interval within a reservoir;     -   selecting locations for packers to fluidically isolate zones in         the interval, wherein the selection is based, at least in part,         on a model of the response of a rock to a stimulation fluid over         a period of time;     -   positioning the packers at the selected locations; and     -   stimulating the reservoir within selected zones using an acid         solution.

B. The method of paragraph A, comprising designing a well to reach the interval within the reservoir.

C. The method of paragraph A, including simulating fluid flow of a stimulation fluid in a well and surrounding a stimulation conduit and surrounding rock.

D. The method of paragraph A, including modeling the influence of an acid solution on the rock.

E. The method of paragraph A, including taking core samples during the drilling or any other suitable logging of the well to map the permeability of the rock along the well.

F. The method of paragraph A, including producing hydrocarbon from the well.

G. The method of paragraph E, including isolating zones of higher permeability rock from zones of lower permeability rock.

H. The method of paragraph E, including acid-treating the zones of lower permeability rock.

I. The method of paragraph A, wherein the zones are less than about 500 meters in length.

J. The method of paragraph A, including modeling the response of a rock in the well to acid stimulation, wherein the modeling provides a time of exposure to the acid solution to obtain a plurality of wormholes of a particular length.

K. The method of paragraph A, including modeling the response of a rock in the well to acid stimulation, wherein the modeling provides a concentration of the acid solution to obtain a plurality of wormholes of a particular size.

L. The method of paragraph A, including modeling the response of a rock in the well to acid stimulation, wherein the modeling provides a length of a stimulation zone.

M. A system for fluid stimulation in wells, including:

-   -   a well drilled through an interval in a reservoir;     -   a plurality of packers placed in the well, wherein a zone is         defined by the location of two sequential packers in the well,         and wherein the location of each of the plurality of packers is         selected from a model of wormhole growth dynamics over time         during an acid stimulation procedure; and     -   a well string configured to convey acid to a zone in the         production interval.

N. The system of paragraph M, wherein the production interval includes a zone including a carbonate rock.

O. The system of paragraph M, wherein the zone is fluidically isolated from an adjoining zone by a packer.

Further embodiments of the claimed subject matter may include the methods and systems disclosed in the following number paragraphs:

1. A method for fluid stimulation of long well intervals, including:

-   -   drilling a well to reach an interval within a reservoir;     -   selecting locations for packers to fluidically isolate zones in         the interval, wherein the selection is based, at least in part,         on a model of the response of a rock to a stimulation fluid over         a period of time;     -   positioning the packers at the selected locations; and     -   stimulating the reservoir within selected zones using an acid         solution.

2. The method of paragraph 1, including designing the well to reach the interval within the reservoir

3. The method of paragraph 1, including simulating fluid flow of a stimulation fluid in a well and surrounding a stimulation conduit and surrounding rock.

4. The method of paragraph 1, including modeling the influence of an acid solution on the rock.

5. The method of paragraph 1, including taking core samples during the drilling or any other suitable logging of the well to map the permeability of the rock along the well.

6. The method of paragraph 1, including producing hydrocarbon from the well.

7. The method of paragraph 1, including isolating zones of higher permeability rock from zones of lower permeability rock.

8. The method of paragraph 5, including acid-treating the zones of lower permeability rock.

9. The method of paragraph 1, including drilling a well that is less than about 3 kilometers in length.

10. The method of paragraph 7, wherein the zones are less than about 500 meters in length.

11. The method of paragraph 1, including modeling the response of a rock in the well to acid stimulation, wherein the modeling provides a time of exposure to the acid solution to obtain a plurality of wormholes of a particular length.

12. The method of paragraph 1, including modeling the response of a rock in the well to acid stimulation, wherein the modeling provides a concentration of the acid solution to obtain a plurality of wormholes of a particular size.

13. The method of paragraph 1, including modeling the response of a rock in the well to acid stimulation, wherein the modeling provides a length of a stimulation zone.

14. A system for fluid stimulation in wells, including:

-   -   a well drilled through an interval in a reservoir;     -   a plurality of packers placed in the well, wherein a zone is         defined by the location of two sequential packers in the well,         and wherein the location of each of the plurality of packers is         selected from a model of wormhole growth dynamics over time         during an acid stimulation procedure; and     -   a well string configured to convey acid to a zone in the         production interval.

15. The system of paragraph 14, wherein the production interval includes a zone including a carbonate rock.

16. The system of paragraph 14, wherein the zone is fluidically isolated from an adjoining zone by a packer.

17. The system of paragraph 14, including a jack-up rig for drilling the well in a sub-sea environment.

18. A method for harvesting hydrocarbons from a production interval, including:

-   -   modeling a well to determine a length of a stimulation zone in         the production interval, wherein the model is based, at least in         part, on a reaction time for a stimulation process;     -   placing packers in the well to fluidically isolate the         stimulation zone from other zones in the well;     -   stimulating the zone by acid treatment; and     -   recovering hydrocarbon from the stimulation zone.

19. The method of paragraph 18, including stimulating only a portion of a plurality of zones in a production interval.

20. The method of paragraph 18, including placing preinstalled packers to isolate a zone including an annulus between a well and a liner.

21. The method of paragraph 18, including placing retractable packers to isolate a zone including an annulus between a drill pipe and a liner.

22. The method of paragraph 18, including placing a retractable packer to isolate a zone by blocking a liner.

23. The method of paragraph 18, including calculating an efficiency curve for a stimulation process for a selected rock type, acid concentration, and temperature.

While the present techniques may be susceptible to various modifications and alternative forms, the embodiments discussed above have been shown only by way of example. However, it should again be understood that the techniques is not intended to be limited to the particular embodiments disclosed herein. Indeed, the present techniques include all alternatives, modifications, and equivalents falling within the true spirit and scope of the appended claims. 

What is claimed is:
 1. A method for fluid stimulation of long well intervals, comprising: drilling a well to reach an interval within a reservoir; selecting locations for packers to fluidically isolate zones in the interval, wherein the selection is based, at least in part, on a model of the response of a rock to a stimulation fluid over a period of time; positioning the packers at the selected locations; and stimulating the reservoir within selected zones using an acid solution.
 2. The method of claim 1, comprising designing the well to reach the interval within the reservoir.
 3. The method of claim 1, comprising simulating fluid flow of a stimulation fluid in a well and surrounding a stimulation conduit and surrounding rock.
 4. The method of claim 1, comprising modeling the influence of an acid solution on the rock.
 5. The method of claim 1, comprising taking core samples during the drilling or any other suitable logging of the well to map the permeability of the rock along the well.
 6. The method of claim 1, comprising producing hydrocarbons from the well.
 7. The method of claim 1, comprising isolating a zone of higher permeability rock from a zone of lower permeability rock.
 8. The method of claim 5, comprising acid-treating the zone of lower permeability rock.
 9. The method of claim 1, comprising drilling a well that is less than about 3 kilometers in length.
 10. The method of claim 7, wherein the zone is less than about 500 meters in length along the well.
 11. The method of claim 1, comprising modeling the response of a rock in the well to acid stimulation, wherein the modeling provides a time of exposure to the acid solution to obtain a plurality of wormholes of a particular length.
 12. The method of claim 1, comprising modeling the response of a rock in the well to acid stimulation, wherein the modeling provides a concentration of the acid solution to obtain a plurality of wormholes of a particular size.
 13. The method of claim 1, comprising modeling the response of a rock in the well to acid stimulation, wherein the modeling provides a length of a stimulation zone.
 14. A system for fluid stimulation in wells, comprising: a well drilled through an interval in a reservoir; a plurality of packers placed in the well, wherein a zone is defined by the location of two sequential packers in the well, and wherein the location of each of the plurality of packers is selected from a model of wormhole growth dynamics over time during an acid stimulation procedure; and a well string configured to convey acid to a zone in the production interval.
 15. The system of claim 14, wherein the production interval comprises a zone comprising a carbonate rock.
 16. The system of claim 14, wherein the zone is fluidically isolated from an adjoining zone by a packer.
 17. The system of claim 14, comprising an offshore rig for drilling the well in a sub-sea environment.
 18. A method for harvesting hydrocarbons from a production interval, comprising: modeling a well to determine a length of a stimulation zone in the production interval, wherein the model is based, at least in part, on a reaction time for a stimulation process; placing packers in the well to fluidically isolate the stimulation zone from other zones in the well; stimulating the zone by acid treatment; and recovering hydrocarbon from the stimulation zone.
 19. The method of claim 18, comprising stimulating only a portion of a plurality of zones in a production interval.
 20. The method of claim 18, comprising placing preinstalled packers to isolate a zone comprising an annulus between a well and a liner.
 21. The method of claim 18, comprising placing retractable packers to isolate a zone comprising an annulus between a drill pipe and a liner.
 22. The method of claim 18, comprising placing a retractable packer to isolate a zone by blocking a liner.
 23. The method of claim 18, comprising calculating an efficiency curve for a stimulation process for a selected rock type, acid concentration, and temperature. 